Scientific investigation of extrasensory perception is complicated by the definition which implies that the phenomena go against established principles of science.[9] Specifically, precognition would violate the principle that an effect cannot occur before its cause.[9] There are established biases affecting human memory and judgment of probability that sometimes create convincing but false impressions of precognition.[10]

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Belief in precognition has been related to superstition.[11] A 1978 Gallup poll found that 37% of Americans surveyed believed in precognition.[12] According to psychologists Tobacyk and Milford, belief in precognition was greater in college women than in men, and a 2007 Gallup poll found that women were more prone to superstitious beliefs in general.[11]

A 2013 study discovered that greater belief in precognition was held by those who feel low in control, and the belief can act as a psychological coping mechanism.[13]

In the early 20th century J. W. Dunne, a British aeronautics engineer, recorded each of his dreams as they occurred to him, identifying any correspondences between his future experiences and his recorded dreams. In 1927, he reported his findings, in An Experiment with Time. In this work, he alleges that 10% of his dreams appeared to represent some future event, pertaining to some relatively trivial incident in his own life, or some major news events appearing in the press after the dream. Dunne concluded that precognitive dreams are common occurrences: he claims that many people have them without realizing it, largely because they do not recall the details of the dream.[14] Dunne also wrote about an experiment he conducted recording the dreams of other participants, and sought to associate them with subsequent experiences. Dunne felt these confirmed his claims, but a 1933 independent experiment failed to replicate his findings.[15]

The first ongoing and organized research program on precognition was instituted by Joseph Banks Rhine in the 1930s at Duke University's Parapsychology Laboratory. Rhine used a method of forced-choice matching in which participants guessed the order of a deck of 25 cards, each five of which bore one of five geometrical symbols. The experiment was not blinded, so participants were able to read the symbols through the back of the cards, and were able to see and hear the experimenters throughout the experiment. This sensory leakage contributed to Rhine's experiments being discredited.[16][17][18]

Experiments by Samuel G. Soal ran forced-choice ESP experiments in which someone attempted to identify which of five animal pictures a subject in another room was looking at. Their performance on this task was at chance, but when the scores were matched with the card that came after the target card, three of the thirteen subjects showed a very high hit rate.[19] Rhine described Soal's work as "a milestone in the field".[19]George Price reviewed the experiment in Science in 1955,[20] and concluded that the positive results not attributable to error were more likely the result of deliberate fraud.[20] This prompted several replies that Price's criticism was unfair.[19] In 1978, the experiments were exposed as fraudulent. The statistician and paragnost Betty Markwick, while seeking to vindicate Soal, discovered that he had altered his data to create all the extra hits and give the study its statistical significance.[20] The untainted experimental results showed no evidence of precognition in the hits or the ratios.[19][21]

Following these experiments, a more automated technique of experimentation was introduced that did not rely on hand-scoring of equivalence between targets and guesses, and in which the targets could be more reliably and readily tested at random. This involved testing for precognition with the use of high-speed random event generators (REG), as introduced by Helmut Schmidt in 1969, and at the Princeton Engineering Anomalies Research Lab.[22] The psychologist C. E. M. Hansel found flaws in all of Schmidt's experiments into precognition. Hansel found that necessary precautions were not taken, there was no presence of an observer or second-experimenter in any of the experiments, no counterchecking of the records and no separate machines used for high and low score attempts.[23]

In 2011, the parapsychologist Daryl Bem published the article "Feeling the Future: Experimental Evidence for Anomalous Retroactive Influences on Cognition and Affect" in the Journal of Personality and Social Psychology that offered statistical evidence for precognition.[24] The article's findings challenged modern scientific conceptions about the unidirectional nature of time. Its presentation by a respected researcher and its publication by an upper tier journal engendered much controversy. In addition to criticism of the paper itself,[25] the paper's publication prompted a wider debate on the validity of peer review process for allowing such a paper to be published.[26] Bem appeared on MSNBC[27] and The Colbert Report[28] to discuss the experiment.

Jeffrey Rouder and Richard Morey who applied a meta-analytical Bayes factor to Bem's data concluded "We remain unconvinced of the viability of ESP. There is no plausible mechanism for it, and it seems contradicted by well-substantiated theories in both physics and biology. Against this background, a change in odds of 40 is negligible.[29][30]

After evaluating Bem's nine experiments, psychologist James Alcock said that he found metaphorical "dirty test tubes," or serious methodological flaws, such as changing the procedures partway through the experiments and combining results of tests with different chances of significance. It is unknown how many tests were actually performed, nor is there an explanation of how it was determined that participants had "settled down" after seeing erotic images. Alcock concludes that almost everything that could go wrong with Bem's experiments did go wrong. Bem's response to Alcock's critique appeared online at the Skeptical Inquirer website[31] and Alcock replied to these comments in a third article at the same website.[32]

In 2012, the same journal that published Bem's original experiments, the Journal of Personality and Social Psychology (Vol. 103, No. 6), published “Correcting the Past: Failures to Replicate Psi” by Jeff Galek of Carnegie Mellon University, Robyn A. LeBoeuf of the University of Florida, Leif D. Nelson of the University of California at Berkeley, and Joseph P. Simmons of the University of Pennsylvania. The paper reported seven experiments testing for precognition that "found no evidence supporting its existence.”[33][34]

There is no known mechanism for precognition.[35] Precognition would violate the principle of antecedence (causality), that an effect does not happen before its cause.[36]

The physicist John Taylor has written "since only positive energies are possible, particles going backward in time cannot exist. Any claim that they do is purely a fantasy in the mind of the parapsychologist. There is therefore no direct justification for precognition from physics... experimental evidence from high energy physics is strongly against it."[37]

Neuroscientist Samuel Schwarzkopf has written that precognition contradicts "most of the neuroscience and psychology literature, from electrophysiology and neuroimaging to temporal effects found in psychophysical research."[38]

Various psychological processes have been offered to explain experiences of apparent precognition. These include:

Selection bias where people remember the "hits" and forget the "misses", remember coincidences more often than other non-coincidences, or when they were correct about a future event rather than instances when they were wrong. Examples include thinking of a specific person before that person calls on the phone. Human memory, it is argued, has a tendency to record instances when the guess was correct, and to dismiss instances when the guess was incorrect.

Unconscious perception by which people unconsciously infer, from data they have unconsciously learned, that a certain event will probably happen in a certain context. As with cryptomnesia, when the event occurs, the former knowledge appears to have been acquired without the aid of recognized channels of information.

Self-fulfilling prophecy and Unconscious enactment in which people bring events that they have precognized to pass, but without their conscious knowledge.

Some psychologists have explained the apparent prevalence of precognitive dreams in terms of memory biases, namely a selective memory for accurate predictions and distorted memory so that dreams are retrospectively fitted onto subsequent events.[10] In one experiment, subjects were asked to write down their dreams in a diary. This prevented the selective memory effect, and the dreams no longer seemed accurate about the future.[39] Another experiment gave subjects a fake diary of a student with apparently precognitive dreams. This diary described events from the person's life, as well as some predictive dreams and some non-predictive dreams. When subjects were asked to recall the dreams they had read, they remembered more of the successful predictions than unsuccessful ones.[40]

An early inquiry into allegedly prophetic dreams was done by Aristotle in his On Divination in Sleep. His criticism of these claims appeals to the fact that "the sender of such dreams should be God", and "the fact that those to whom he sends them are not the best and wisest, but merely commonplace persons." Thus: "Most [so-called prophetic] dreams are, however, to be classed as mere coincidences...", here "coincidence" being defined by Aristotle as that which does not take "place according to a universal or general rule" and referring to things which are not of themselves by necessity causally connected. His example being taking a walk during an eclipse, neither the walk nor the eclipse being apparently causally connected and so only by "coincidence" do they occur simultaneously.[41]

In 1932 Charles Lindbergh's infant son was kidnapped and murdered. The psychologists Henry Murray and D. R. Wheeler tested precognitive dreams by inviting the public to report any dreams of the child. A total of 1,300 dreams were reported. Only five percent envisioned the child dead and only 4 of the 1,300 envisioned the location of the body as buried amongst trees. This number was no better than chance.[42]

David Ryback, a psychologist in Atlanta, used a questionnaire survey approach to investigate precognitive dreaming in college students. His survey of over 433 participants showed that 290 or 66.9 percent reported some form of paranormal dream. He rejected many of these reports, but claimed that 8.8 percent of the population was having actual precognitive dreams.[43]

Suppose that you can remember ten incidents from a night's dreaming, at least when prompted by a similar incident occurring a day. Now consider how many incidents occur during a day, including those you read about in the paper, watch on television or hear from your friends. There are a vast number and it is highly probable that from time to time one of them will, at least to some extent, resemble one of those from your dreams. When one or more of these coincidences occur, people are likely to conclude that dreams foretell the future.[45]

Robert Todd Carroll, author of The Skeptic's Dictionary put it this way: "Say the odds are a million to one that when a person has a dream of an airplane crash, there is an airplane crash the next day. With 6 billion people having an average of 250 dream themes each per night, there should be about 1.5 million people a day who have dreams that seem clairvoyant."[46]

^Bunge, Mario. (1983). Treatise on Basic Philosophy: Volume 6: Epistemology & Methodology II: Understanding the World. Springer. p. 226. "Despite being several thousand years old, and having attracted a large number of researchers over the past hundred years, we owe no single firm finding to parapsychology: no hard data on telepathy, clairvoyance, precognition, or psychokinesis."

^Stenger, Victor. (1990). Physics and Psychics: The Search for a World Beyond the Senses. Prometheus Books. p. 166. ISBN 0-87975-575-X "The bottom line is simple: science is based on consensus, and at present a scientific consensus that psychic phenomena exist is still not established."

^Zechmeister, Eugene; Johnson, James. (1992). Critical Thinking: A Functional Approach. Brooks/Cole Pub. Co. p. 115. ISBN 0534165966 "There exists no good scientific evidence for the existence of paranormal phenomena such as ESP. To be acceptable to the scientific community, evidence must be both valid and reliable."

^Myers, David. (2004). Intuition: Its Powers and Perils. Yale University Press. p. 233. ISBN 0-300-09531-7 "After thousands of experiments, no reproducible ESP phenomenon has ever been discovered, nor has any researcher produced any individual who can convincingly demonstrate psychic ability."

^Harold Gulliksen. (1938). Extra-Sensory Perception: What Is It?. American Journal of Sociology. Vol. 43, No. 4. pp. 623-634. "Investigating Rhine's methods, we find that his mathematical methods are wrong and that the effect of this error would in some cases be negligible and in others very marked. We find that many of his experiments were set up in a manner which would tend to increase, instead of to diminish, the possibility of systematic clerical errors; and lastly, that the ESP cards can be read from the back."

^Charles M. Wynn, Arthur W. Wiggins. (2001). Quantum Leaps in the Wrong Direction: Where Real Science Ends...and Pseudoscience Begins. Joseph Henry Press. p. 156. ISBN 978-0-309-07309-7 "In 1940, Rhine coauthored a book, Extrasensory Perception After Sixty Years in which he suggested that something more than mere guess work was involved in his experiments. He was right! It is now known that the experiments conducted in his laboratory contained serious methodological flaws. Tests often took place with minimal or no screening between the subject and the person administering the test. Subjects could see the backs of cards that were later discovered to be so cheaply printed that a faint outline of the symbol could be seen. Furthermore, in face-to-face tests, subjects could see card faces reflected in the tester’s eyeglasses or cornea. They were even able to (consciously or unconsciously) pick up clues from the tester’s facial expression and voice inflection. In addition, an observant subject could identify the cards by certain irregularities like warped edges, spots on the backs, or design imperfections."

^Terence Hines. (2003). Pseudoscience and the Paranormal. Prometheus Books. p. 122. ISBN 1-57392-979-4 "The procedural errors in the Rhine experiments have been extremely damaging to his claims to have demonstrated the existence of ESP. Equally damaging has been the fact that the results have not replicated when the experiments have been conducted in other laboratories."

^Wynn, Charles; Wiggins, Arthur. (2001). Quantum Leaps in the Wrong Direction: Where Real Science Ends...and Pseudoscience Begins. Joseph Henry Press. p. 165. ISBN 978-0309073097 "One of the reasons scientists have difficulty believing that psi effects are real is that there is no known mechanism by which they could occur. PK action-at-a-distance would presumably employ an action-at-a-distance force that is as yet unknown to science... Similarly, there is no known sense (stimulation and receptor) by which thoughts could travel from one person to another by which the mind could project itself elsewhere in the present, future, or past."

"In short, you have lots of dreams and encounter lots of events. Most of the time the dreams are unrelated to the events, and so you forget about them. However, once in a while one of the dreams will correspond to one of the events. Once this happens, it is suddenly easy to remember the dream and convince yourself that it has magically predicted the future. In reality, it is just the laws of probability at work."

"The principle is known as the ‘Law of Large Numbers’, and states that unusual events are likely to happen when there are lots of opportunities for that event. It is exactly the same with any national lottery. The chances of any one person hitting the jackpot is millions to one, but still it happens as regular as clockwork each week because such a large number of people buy tickets. For genuine evidence of premonitions then, the situation is even worse than we have imagined... Given that people dream about doom and gloom more often than not, the numbers quickly stack up and acts of apparent prophecy are inevitable."